OSA's Digital Library

Journal of the Optical Society of America B

Journal of the Optical Society of America B

| OPTICAL PHYSICS

  • Vol. 8, Iss. 1 — Jan. 1, 1991
  • pp: 106–113

Multistability and associative memory in a phase-conjugating resonator

Marcus S. Cohen  »View Author Affiliations


JOSA B, Vol. 8, Issue 1, pp. 106-113 (1991)
http://dx.doi.org/10.1364/JOSAB.8.000106


View Full Text Article

Acrobat PDF (1005 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

I derive and analyze coupled-mode equations for a double phase-conjugating resonator that is loaded with a volume-holographic recording medium in which multiplexed images have been stored. If the only nonlinearity present is the saturating gain of the conjugators, there is no multistability: The most deeply imprinted image always wins the competition for saturation. If several images are imprinted with equal depth, any slowly varying superposition of these images is neutrally stable. However, if a nonlinearity, arising from a space-chargedependent cubic polarization, is present the resonator does exhibit multiple basins of stability that correspond to the faithful reconstruction of each stored image. The momentary injection of an initial image will tip the system into the basin that corresponds to the stored image that it most closely resembles, even if that image is not the most deeply imprinted one.

© 1991 Optical Society of America

Citation
Marcus S. Cohen, "Multistability and associative memory in a phase-conjugating resonator," J. Opt. Soc. Am. B 8, 106-113 (1991)
http://www.opticsinfobase.org/josab/abstract.cfm?URI=josab-8-1-106


Sort:  Author  |  Year  |  Journal  |  Reset

References

  1. M. S. Cohen, "Self organization categorization, and abstraction in a phase conjugating resonator," in Optical Computing, J. A. Neff, ed., Proc. Soc. Photo-Opt. Instrum. Eng. 625, 214–219 (1986).
  2. M. S. Cohen, "Multiple correlations in holographic resonators," in Neural Networks for Optical Computing, R. A. Athale and J. Davis, eds., Proc. Soc. Photo-Opt. Instrum. Eng. 882, 122–131 (1988).
  3. B. H. Soffer, G. J. Dunning, Y. Owechko, and E. Marom, "Associative holographic memory with feedback using phase conjugate mirrors," Opt. Lett. 11, 118–120 (1986).
  4. D. Z. Anderson and C. E. Marie, "Resonator memories and optical novelty filters," Opt. Eng. 26, 434–444 (1987).
  5. M. S. Cohen, "Design of a new medium for volume holographic information processing," Appl. Opt. 25, 2288–2294 (1986).
  6. M. S. Cohen and W. H. Julian, "Multistability, chains, and cycles in optical multiwave mixing processes," Appl. Opt. (to be published).
  7. A. E. Siegman, P. A. Belanger, and A. Hardy, "Optical resonators using phase-conjugating mirrors," in Optical Phase Conjugation, R. A. Fisher, ed. (Academic, New York, 1983), pp. 465–535.
  8. A. C. Newell, "Bifurcation and nonlinear focusing," in Pattern Formation and Pattern Recognition, H. Haken, ed. (Springer-Verlag, Berlin, 1980), pp. 244–265.
  9. M. Schubert and B. Wilhelmi, Nonlinear Optics and Quantum Electronics (Wiley, New York, 1986).
  10. N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskuv, V. L. Vinetskii, "Holographic storage in electro-optic crystals," Ferroelectrics 22, 949 (1979).
  11. P. Refregier, C. Solymar, H. Rajbenbach, and H. P. Huignard, "Two-beam coupling in photorefractive Bi12SiO20 crystals with moving grating: theory and experiments," J. Appl. Phys. 58, 45–57 (1985).
  12. A. Borshch, M. Brodin, V. Volkov, N. Kukhtarev, and V. Starkov, "Optical phase conjugation by degenerate sixphoton mixing," J. Opt. Soc. Am. A 1, 40 (1984).
  13. J. Hopfield, "Neural networks and physical systems with emergent collective computational abilities," Proc. Natl. Acad. Sci. USA 79, 2554–2558 (1984).
  14. D. L. Bobroff and H. A. Haus, "Impulse response of active coupled wave systems," J. Appl. Phys. 38, 390–403 (1967).
  15. W. W. Rigrod, R. A. Fisher, and B. J. Feldman, "Transient analysis of nearly degenerate four-wave mixing," Opt. Lett. 5, 105–107 (1980).
  16. R. A. Fisher, B. R. Suydam, and B. J. Feldman, "Transient analysis of Kerr-like phase conjugators using frequencydomain techniques," Phys. Rev. A, 23, 3071–3083 (1981).
  17. F. John, Partial Differential Equations (Springer-Verlag, New York, 1982), p. 48.
  18. M. Sargent, M. O. Scully, and W. Lamb, Laser Physics (Addison-Wesley, New York, 1987).

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited